Two friends go to the cinema and buy two tickets, two regular boxes of popcorn, two slush puppies and a packet of whispers.They decide to equally split the total cost, resulting in each friend...

Two friends go to the cinema and buy two tickets, two regular boxes of popcorn, two slush puppies and a packet of whispers.

They decide to equally split the total cost, resulting in each friend paying $56.00. If a movie ticket costs $10.00 more than a box of popcorn, which in turn costs $3.00 more than a slush puppie, which in turn costs $4.00 more than a packet of whispers. Determine the cost of a movie ticket, a box of popcorn, a slush puppie and a packet of whispers.

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kjcdb8er | Teacher | (Level 1) Associate Educator

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The friends together spend 56*2 = 112 on two tickets (t), two popcorns (p), two slushes (s), and one whispers (w). So,

2t + 2p + 2s + w = 112            Also, we have:

t - p = 10

p - s = 3

s - w = 4

 

You can solve this by isolating variables and plugging in. But we can also solve this by putting it in matrix form and transforming it to row echelon form:

2t + 2p + 2s + 1w = 112

1t - 1p + 0s + 0w  = 10

0t + 1p - 1s + 0w = 3

0t + 0p + 1s - 1w = 4               or,

 

[ 2 2 2 1 | 112                               [ 1 0 0 0 | 25

1 -1 0 0 | 10            -->                   0 1 0 0 | 15

0 1 -1 0 | 3                                     0 0 1 0 | 12

0 0 1 -1 | 4]                                    0 0 0 1 | 8 ]

 

So t = 25, p = 15, s = 12, and w = 8

You can check the answer to see how this checks out.

 

For a review on how to reduce a matrix to echelon form, you do the following:

Step 1: divide row 1 so that leading number is 1

Step 2: multiply and add so that the column of the leading number is zero in all other rows.

Step 3: repeat for each row.

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